Limit of Detection Calculator
Compute limit detection using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
LOD = 3.3 x SD / Slope | LOQ = 10 x SD / Slope
The LOD is calculated as 3.3 times the standard deviation (of blanks or residuals) divided by the calibration curve slope. LOQ uses a factor of 10 instead of 3.3. The 3.3 factor corresponds to approximately 99% confidence for detection.
Worked Examples
Example 1: LOD from Blank Measurements
Problem:Twenty blank samples have a mean response of 0.025 absorbance units and a standard deviation of 0.003. Calculate LOD and LOQ.
Solution:LOD = Mean(blank) + 3.3 x SD(blank)\nLOD = 0.025 + 3.3 x 0.003\nLOD = 0.025 + 0.0099 = 0.0349 absorbance units\n\nLOQ = Mean(blank) + 10 x SD(blank)\nLOQ = 0.025 + 10 x 0.003 = 0.055 absorbance units
Result:LOD = 0.0349 AU | LOQ = 0.0550 AU
Example 2: LOD from Calibration Curve (ICH Method)
Problem:A calibration curve has slope = 0.45 AU/(mg/L) and residual standard deviation = 0.004 AU. Calculate LOD and LOQ.
Solution:LOD = (3.3 x SD_residual) / Slope\nLOD = (3.3 x 0.004) / 0.45\nLOD = 0.0132 / 0.45 = 0.02933 mg/L\n\nLOQ = (10 x SD_residual) / Slope\nLOQ = (10 x 0.004) / 0.45 = 0.08889 mg/L
Result:LOD = 0.0293 mg/L | LOQ = 0.0889 mg/L
Frequently Asked Questions
What is the Limit of Detection (LOD) in analytical chemistry?
The Limit of Detection is the lowest concentration of an analyte that can be reliably distinguished from a blank (zero concentration) but not necessarily quantified with acceptable precision. It represents the minimum signal that can be detected above the background noise with a specified confidence level, typically 99% (corresponding to a factor of 3.3 standard deviations). LOD is a critical parameter in method validation for pharmaceutical analysis, environmental monitoring, food safety testing, clinical diagnostics, and forensic science. A method with a lower LOD is considered more sensitive. LOD should not be confused with the Limit of Quantitation (LOQ), which is the lowest concentration that can be measured with acceptable accuracy and precision.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy